What is the integral from-3/2 to 3/2 of x^3-x+2 ?

The integral from-3/2 to 3/2 of x^3-x+2 is 6

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integral from-3/2 to 3/2 of x^3-x+2

\int_{- \frac{3}{2}}^{\frac{3}{2}} x^{3} - x + 2 d x

6

Solution steps

\int_{- \frac{3}{2}}^{\frac{3}{2}} x^{3} - x + 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- \frac{3}{2}}^{\frac{3}{2}} x^{3} d x - \int_{- \frac{3}{2}}^{\frac{3}{2}} x d x + \int_{- \frac{3}{2}}^{\frac{3}{2}} 2 d x

\int_{- \frac{3}{2}}^{\frac{3}{2}} x^{3} d x = 0

\int_{- \frac{3}{2}}^{\frac{3}{2}} x d x = 0

\int_{- \frac{3}{2}}^{\frac{3}{2}} 2 d x = 6

= 0 - 0 + 6

Simplify

= 6

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What is the integral from-3/2 to 3/2 of x^3-x+2 ?
The integral from-3/2 to 3/2 of x^3-x+2 is 6